All he value of `k` for which the quadratic polynomial `f(x)=2x^2+k x+k^2+5` has two distinct zeroes and only one of them satisfying `0

Answer

7

Explanation

For two distincet roots, `Dgt0i.e.,k^(2)+8(k^(2)+5)gt0` which is always true
Also let `f(x)=-2x^(2)+kx+k^(2)+5=0`
But `f(0)gt0.So, f(2)lt0`
`-8+2k+k^(2)+5lt0`
`impliesk^(2)+2k-3lt0`
`implies (k+3)(k-1)lt0`
`kin(-3,1)`
`impliesa=-3,b=1`
`a+10b=-3+10=7`